Amesbury's first-half hat-trick fired England into a 19-7 half-time lead before the former England under 18 grabbed a fourth after the restart to hand England, who beat hosts Hong Kong 38-7 in Group E on Friday, eased into a commanding lead.
Gloucester's Jack Adams, making his Sevens debut in Hong Kong, and London Irish's Nils Mordt extended the lead in the second half after Amesbury was withdrawn ahead of the final group game against Argentina this evening.
Scotland ran in nine tries as Stephen Gemmell's side put themselves in a strong position in Group A following a 53-21 victory against spirited Sri Lanka on Saturday.
Glasgow Warriors' Mike Adamson and Border Reivers duo Graham Hogg and Scott Forrest each ran in a brace of tries, while Roddy Grant, Jamie Hunter and Max Evans also crossed.
Wales recovered from their disappointing 33-7 defeat by Tonga on Friday and also ran in nine tries during a resounding 61-0 triumph against Chinese Taipei in Group B.
Llanelli duo Jon Edwards and Alec Jenkins contributed two tries, while Dai Flannagan, Rhodri McAtee, Tal Selley, Richard Mustoe and Lee Beach also touched down.
China produced a shock in the third match of the day in Group C with a 21-19 victory over Canada following their valiant effort in losing 49-5 to powerhouse Samoa on Friday.
Italy came from behind to beat Kenya 19-5 in Group D, while in England's Group, Argentina overcame a resilient Hong Kong 19-12.
Australia, who were forced to come from behind to beat Tunisia 19-12 on Friday in Group F, battled back from 14-5 down at the start of the second half to edge out the USA 15-14 courtesy of Josh Holmes try with just 11 seconds remaining.
Portugal took an early lead in their Group A meeting with powerhouses Fiji and were level at 7-7 at the break, but the San Diego winners scored 21 unanswered points after the break to secure victory.
South Africa were also forced to overturn a half-time deficit, coming back from 12-5 behind to beat Tonga 31-12 in Group A courtesy of a hat-trick from Stefan Basson, Samoa eased to a 54-7 victory over Japan and New Zealand also maintained their unbeaten record with a 54-0 triumph against Russia.